THREE-DIMENSIONAL FDTD ANALYSIS OF THE DUAL-BAND IMPLANTABLE ANTENNA FOR CONTIN-UOUS GLUCOSE MONITORING
Z. Noroozi* and F. Hojjat-Kashani
Department of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran
Abstract—The finite difference time domain (FDTD) method is widely used as a computational tool to simulate the electromagnetic wave propagation in biological tissues. When expressed in terms of Debye parameters, dispersive biological tissues dielectric properties can be efficiently incorporated into FDTD codes. In this paper, FDTD formulation with nonuniform grid is presented to simulate a dual medical implant communications service (MICS) (402–405 MHz) and industrial, scientific, and medical (ISM) (2.4–2.48 GHz) band implantable antenna for continuous glucose-monitoring applications. In addition, we present computationally simpler two-pole Debye models that retain the high accuracy of the Cole-Cole Model for dry skin in MICS and ISM bands. The reflection coefficient simulation result with Debye dispersion is presented and compared with the published results. FDTD was also applied to analyze antenna’s far-field.
Recently, with the advances in telecommunications and telemedicine, implantable antennas are studied for several wireless applications such as artificial eyes, cochlear implants, brain and cardiac pacemakers [1– 3], implantable drug pumps, hyperthermia treatment , etc. Scanlon et al.  performed numerical simulations for a printed loop antenna in a whole body phantom model (chest) at 418 MHz. Implantable antennas were the subject of a study reported by Kim and Rahmat-Samii . In this study, they have designed a spiral microstrip and planar inverted-F antennas (PIFAs) at the MICS band based on the
Received 1 July 2011, Accepted 15 August 2011, Scheduled 29 November 2011
FDTD simulations. They have also reported simulation results (based on FDTD) of the maximum available received power by an external (to the body) dipole antenna. Soontornpipit et al. , evaluated s11
of spiral and serpentine antennas at the MICS band. In a study by Warty and Tofighi , characterization of implantable PIFAs, designed for intracranial pressure (ICP) monitoring at 2.45 GHz, has been presented. In , an H-shaped cavity slot antenna was miniaturized and the characteristics of the antenna calculated by the FDTD method at the ISM band.
FDTD method, has become a popular numerical technique for analyzing the propagation of electromagnetic fields in the human body. For narrowband computations, the standard FDTD algorithm for lossy dielectric media can be used for biological tissues with acceptable accuracy. However, in broadband simulations by using a pulsed excitation, it is necessary to use time domain updating equations which incorporate the variation in the dielectric properties of tissues with frequency. Precise frequency dependent permittivity and conductivity values for biological tissues have been made available by Gabriel et al. that have been fitted by relatively complicated 4-pole Cole-Cole equations [10–12]. However, the implementation of the Cole-Cole model using the FDTD method is difficult because of the fractional order differentiators in this model. In some studies, least squares fitting technique has been applied to reduce Gabriel’s 4-pole Cole-Cole equations to simpler 2-4-pole Debye equations [13–15]. In , a new FDTD formulation is presented for the modeling of electromagnetic wave propagation in dispersive biological tissues with the Cole-Cole model and the Z-transform is used to represent the frequency dependent dielectric properties.
This paper presents a two-step procedure for accurate simulation of a dual-band implantable antenna in dispersive media into the FDTD formulation. First, we present Debye parameters that describe the dispersive dielectric properties of dry skin tissue over considered frequency range (from 0.3 GHz to 3 GHz). The procedure employed here for fitting a Debye model to Cole-Cole data was previously described in . Then FDTD formulation with nonuniform grid based on the Auxiliary Differential Equation Method (ADE) in conjuction with convolutional perfectly matched layered (CPML) is employed to simulate the dual-band implantable antenna for continuous glucose-monitoring applications  at the MICS and ISM bands. The resonance characteristics (in terms of s11) of the dual-band antenna
transformation technique .
2. TWO-POLE DEBYE DISPERSION MODEL OF HUMAN DRY SKIN
The general form of Cole-Cole formulation for the relative complex permittivity ˆε(ω) is given in  as
1 + (jωτn)(1−αn) +
whereε∞is the high frequency permittivity,τn is the relaxation time,
∆εnis the pole amplitude,αnis the pole broadening andσis the static
ionic conductivity. The required general form of the Debye formulation is ˆ ε(ω) =ε∞+ N X n=1
1 + jωτn + σ
Using the “residues” Matlab procedure, the Debye coefficients (εs,
τn, ∆εn and σ) were obtained and tabulated for 16 human tissues in the frequency range 0.75–250 MHz . In this research, this procedure was applied to obtain complex permittivity of dry skin. The actual measurement data from  have been used instead of the Cole-Cole equation. The two-term Debye representation was sufficient to fit the data with an reliable error in the frequency range 0.3–3 GHz. The coefficients are given in Table 1.
In addition, we calculated the errors in the real and imaginary parts of the complex relative permittivity.
er(ω) =ε0d(ω)−ε0c(ω) (3)
ei(ω) =ε00d(ω)−ε00c(ω) (4)
Table 1. Debye parameters for dry skin in the frequency range 0.3– 3 GHz.
Debye parameters Values for dry skin
∆ε2 121.0454 τ1 [s] 0.011×10−9 τ2 [s] 1.458×10−9
Figure 1. Error between the fitted measurement data  and a two-pole Debye model of dry skin with the parameters given in Table 1.
Figure 1 shows the errors in the real and imaginary parts of the relative permittivity as defined in (3) and (4) for the two-pole Debye model of dry skin from 0.3 to 3 GHz. For this model, the error is extremely small (0.02%).
3. A BRIEF REVIEW OF THE DUAL-BAND IMPLANTABLE ANTENNA
In , a dual-band implantable antenna intended for continuous glucose-monitoring applications was designed andin vitro tested. The top and side views of the initial antenna design are shown in Figs. 2(a) and (b), respectively. A serpentine configuration was considered for optimizing the antenna surface area and a shorting pin was used to assist in antenna miniaturization. This procedure typically produces the same frequency response at less than half the size of a similar antenna without the shorting pin . Rogers RO3210 (εr = 10.2,
tanδ = 0.003) was used for the substrate and superstrate material. To tune and improve the antenna characteristics, at the MICS and ISM bands, particle swarm optimization (PSO) was applied. The length and width of the substrate were kept constant atLsub=Wsub=
22.5 mm. The patch length and width also remained constant at
Lp = 22 mm and Wp = 17.75 mm. Any remaining parameters were
considered dimensions in the solution space.
For the optimization procedure, the antenna geometry was organized as shown in Fig. 3.
Figure 2. (a) Top and (b) side views of the initial antenna.
Figure 3. Optimization
parame-ters . Figure 4.ison of the initial and optimizedReturn-loss compar-antenna designs .
function for PSO was defined as
Table 2. Optimization parameters.
Symbol Optimized (mm)
optimized antenna to the initial design. The optimized antenna was fabricated and measured in a skin mimicking gel. The simulated and measured bandwidths were found to be 20.4% MICS, 4.2% ISM, and 35.3% MICS, and 7.1% ISM, respectively.
4. FDTD ANALYSIS OF DUAL-BAND IMPLANTABLE ANTENNA
4.1. Define Problem Space
Figure 5. FDTD problem space.
in the considered frequency range. Voltage and current are sampled across and around the voltage source, and they are tied together to form input port.
4.2. FDTD Subcell Modeling
Subcell modeling is often used in FDTD to model structures with dimensions much smaller than those of other elements in the overall grid. This method, resides on the idea of the contour path modeling technique which uses the integral form of Faraday’s and Ampere’s laws. To precisely model the antenna structure here, we have applied two subcell modeling techniques: the thin-sheet model (to model the zero thickness PEC objects include the radiator and the ground plane) and the thin wire model (to model the inner conductor of coaxial probe and the shortening pin).
In , a simple thin-sheet modeling technique with a reasonable accuracy for the majority of problems including zero thickness PEC strips, was discussed. In this method, any electric conductivity components surrounding and coinciding with PEC plates can be assigned the conductivity of PEC to model zero thickness PEC plates in FDTD method. The standard FDTD notation for the thin wire model can be found in [19, 24].
4.3. Radiation Pattern Computation
In FDTD method, the direct evalution of the far field calls for an excessively large computational domain, which is not practical in applications. Instead, the far-zone electromagnetic fields are computed from NF-FF transformation by integrating the tangential field on a Huygens’ box . In this work, far fields for all observation angles are required for 402 MHz and 2.4 GHz. For each frequency of interest a running Discrete Fourier Transform (DFT) of the tangential fields (surface currents) on a closed surface is updated at each time step. The complex frequency-domain currents obtained from the DFT are then used to compute the far fields at all observation angles through the frequency-domain transformation . To obtain necessary surface currents, the selected surface is a rectangular box that it’s faces are 13 cells away from the outer boundaries, thus 3 cells away from the CPML interface and residing in the air gap region.
4.4. FDTD Results
Calculated. The voltage between the ground plane and the probe is evaluated as a line integral of the electric field, while the current induced on the probe is obtained via a contour integral of the circumferential magnetic field around the probe. The calculated return loss is plotted in Fig. 6 and shows a good agreement with Fig. 4 (the published measurements data in ). The−10 dB bandwidths of the FDTD simulation in the MICS and ISM regions are 20.8% and 7%, respectively.
Furthermore, the directivity patterns are calculated in thexy,xz, andyzPlane cuts at 402 MHz and 2.4 GHz. These patterns are plotted in Figs. 7, 8, and 9, respectively. The results for 402 MHz are consistent with the gain characteristics of the MICS band implantable microstrip antennas in the literature .
Figure 6. Return loss of the dual-band implantable antenna (FDTD result).
(a) 402 MHz (b) 2.4 MHz
(a) 402 MHz (b) 2.4 MHz
Figure 8. Radiation patterns in the xz plane cut.
(a) 402 MHz (b) 2.4 MHz
Figure 9. Radiation patterns in the yz plane cut.
skin. The result shows a good agreement with the published measurements data. Furthermore, the directivity patterns were calculated in the xy, xz, and yz plane cuts at 402 MHz and 2.4 GHz.
We are currently working to calculate antenna radiation efficiency and the maximum delivered power for SAR considerations.
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